He signed for a $1,550,000 bonus. He made his pro debut that year with the AZL Brewers, where he went 2-5 with a 5.88 ERA in 13 appearances. Despite his numbers and thanks to his fastball hitting 100 mph at times, Baseball America rated him as the Arizona League's #2 prospect after Hank Conger and just ahead of Cedric Hunter, the MVP.

With the 2007 West Virginia Power, Jeremy was 9-5 with a 3.13 ERA and 95 strikeouts in 86 1/3 innings. He allowed a .201 average but walked 44 and led the South Atlantic League with five balks. On August 30, he was suspended for 50 games for violating the Minor League Drug Treatment and Prevention Program after testing positive for marijuana. Baseball America did not rate him as one of the SAL's top 20 prospects but did rank him 4th among Milwaukee farmhands.

In 2009, the Virginian hurler walked 55 and fanned 70 in 60 1/3 innings for Huntsville (1-3, 7.57) and Brevard County (2-1, 2.18). He was handed a 100-game suspension for his second positive marijuana test. Upon returning from his suspension in 2010, Jeffress was moved to the bullpen. He pitched for the Wisconsin Timber Rattlers (eight hitless, scoreless innings, 14 K), Brevard County (Sv, 5.40, 7 BB, 14 K in 10 IP) and Huntsville (1-1, 3 Sv, 1.26, 15 K in 14 1/3 IP). Despite never having pitched in AAA, his fine AA work and his velocity earned him a September call-up that year.

Jeffress made his major league debut with the Brewers in 2010. In his first outing in The Show, he entered with a 6-1 deficit in the bottom of the 8th against the Cincinnati Reds. He gave up a leadoff single to Miguel Cairo but Paul Janish grounded into a double play and Ryan Hanigan grounded out to end the frame. He pitched 10 games that season, with 1 win and a 2.70 ERA in 10 innings.

In December 2010, Jeffress was traded to the Kansas City Royals with Alcides Escobar, Lorenzo Cain, and Jake Odorizzi for Zack Greinke, Yuniesky Betancourt and cash. He spent most of the 2011 season in the minors, going 1-3, 4.26 in 9 games for the AA Northwest Arkansas Naturals and 2-3, 7.12 in 16 games for the AAA Omaha Storm Chasers. He served a second suspension for dabbling with marijuana, and in his brief appearances in the majors, failed to impress much, with a record of 1-1, 4.70 and a save in 14 appearances, during which he managed to walk 11 batters in 15 1/3 innings. He was back in the minor leagues again for most of 2012, going 5-4, 4.97 in 37 games for Omaha, also pitching once for Northwest Arkansas. He continued to struggle with his control in his 13 appearances out of the Royals' bullpen, as he walked 13 batters in 13 1/3 innings, contributing to an ERA of 6.75. He also ran into more off-field trouble, being arrested for domestic assault and criminal damage. Although the charges were eventually dropped, he was ordered to issue a formal apology and perform 20 hours of community service for disorderly conduct. After the season, the Royals sold his contract to the Toronto Blue Jays on November 8th.

Jeffress made the Jays' staff out of spring training in 2013, but his stay with the big league team was short-lived. In his first appearance of the year on April 5th, he gave up a run on a hit (a solo homer by Will Middlebrooks), then issued a pair of walks in one inning of relief in a 6-4 loss to the Boston Red Sox. He was designated for assignment after the game, making way for veteran David Bush to make his return to the big leagues.